Two materials overlapping each other in a weird way
You say that moving each face individually would take too long, but you can avoid that problem by moving them all at once:

Select all your objects in Object Mode.

Press Tab to enter Edit Mode and A to select all faces.

Press AltS to perform shrink/fatten, which moves faces along their normals.

Type a small, negative value like -0.01 and press Enter to confirm. (Depending on the details of your geometry, you may also want to try the Offset Even option in the operator panel, which could produce slightly nicer results.)


Now all your objects will be very slightly smaller, avoiding the overlapping faces.